Residency regulations vary from state to state. My suggestion is to contact the financial aid coordinator at the dental school you are considering to simply find out how residency is determined in their state.
I do know that some states require residency be established (driver's license, voter's registration, etc. prior to March 1 of the year prior to the anticipated date of entry. In other words, if you were beginning dental school in August 2004, you would have had to establish residency prior to March 1, 2003.
In other states, it may be as simple as becoming a real estate owner.
Then again, some schools (I believe the University of Michigan; however, I do not know this for certain as I have not yet contacted them), consider state residency by the location of the high school you attended.
Again, contact the school directly (FA office, as they are aware of award regulations).